Turbo equalization is an iterative equalization and decoding technique that enhances performance over frequency selective channels. See, for example, G. Berardinelli, et al., “Improving SC-FDMA Performance by Turbo Equalization in UTRA LTE Uplink”, IEEE VTC Spring 2008, and R. Koetter, et al., “Turbo Equalization”, IEEE Signal Processing Magazine, Volume 21, Issue 1, January 2004.
Compared to linear receivers where the equalization and decoding is done separately, Turbo equalization allows joint equalization and decoding by utilizing the result after tentative decoding to improve equalization by subtracting inter-symbol interference. For MIMO transmission, a similar technique known as Turbo soft interference cancellation (Turbo SIC) can be used to improve equalization by subtracting inter-stream interference. See, for example, G. Berardinelli, et al., “Turbo Receivers for Single User MIMO LTE-A Uplink”, IEEE VTC Spring 2009.
In Turbo equalization and/or soft interference cancellation, an iterative loop is used over the equalization, decoding and signal regeneration. In the soft modulation step, regenerated symbol values are calculated for each symbol as
                    s        ^            n        =                  E        ⁢                  {                      s            n                    }                    =                        ∑                      i            =            0                                M            -            1                          ⁢                              s            i                    ⁢                      P            ⁡                          (                                                s                  n                                =                                  s                  i                                            )                                            ,where si is the transmitted symbol constellation for i=0, . . . , M−1. Here, the input to the soft modulation is the probabilities for each bit after decoding. Thus the symbol probability equals the product of the corresponding bit probabilities, which gives
                    s        ^            n        =                            ∑                      i            =            0                                M            -            1                          ⁢                              s            i                    ⁢                      P            ⁡                          (                                                s                  n                                =                                  s                  i                                            )                                          =                        ∑                      i            =            0                                M            -            1                          ⁢                  (                                    s              i                        ⁢                                          ∏                                  k                  =                  0                                                  q                  -                  1                                            ⁢                              P                ⁡                                  (                                                            b                                              n                        ,                        k                                                              =                                          b                      k                      i                                                        )                                                              )                      ,where q=log2 M is the number of bits per symbol.
With the above expression, the soft modulation step has a high computational complexity. For example, with 16-QAM modulation each soft modulated symbol requires calculating 16 probabilities and multiplying them with the corresponding constellation point and taking the sum of these products. Such computations contribute significantly to the total receiver complexity.